The intrinsic Lipschitz graphs in Theorems REF  and REF  are obtained by modifying a process for constructing intrinsic graphs which appeared recently in [1]}. The method introduced in [1]} produces bumpy intrinsic graphs which are far from vertical planes at many scales. However, the intrinsic gradients of the intrinsic graphs produced in [1]} are \(L_2\) –bounded but not bounded, so the resulting intrinsic graphs are not intrinsic Lipschitz. We overcome this obstacle by applying a stopping time argument leading to intrinsic Lipschtz graphs which retain key properties of the examples from [1]}.
